On the convexity of the value function in Bayesian optimal control problems

Summary I study the question on the convexity of the value function and Blackwell (1951)'s Theorem and relate this to the uniqueness of optimal policies. The main results will conclude that strict convexity and a strict inequality in Blackwell's Theorem will hold if and only if from different priors different optimal actions may be chosen.Financial support from the C. V. Starr Center and the Research Challenge Fund at New York University is gratefully acknowledged. I thank Professor Tara Vishwanathan whose questioning resulted in this paper.